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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 854 · 40 sums
TalentJR

The trick (Ekadhikena Purvena): 2, 5, 10: the last digit (even; 0 or 5; 0). 3 and 9: add the digits. 4: the last two digits. 8: the last three digits. 6: even and passes the rule for 3. 11: from the right, add the 1st, 3rd, 5th… digits and the 2nd, 4th… digits; the difference must be 0 or a multiple of 11. Any prime p: multiply p by 1, 3, 7 or 9 so it ends in 9; one more than the digits before the 9 is the osculator (7 → 5, 13 → 4, 17 → 12, 19 → 2, 23 → 7, 29 → 3). Take the last digit × the osculator and add it to the rest; repeat until the number is small and check the times table. Composite numbers: split into two factors that share no factor and pass BOTH rules — 6 = 2 × 3, 12 = 3 × 4, 15 = 3 × 5, 18 = 2 × 9, 20 = 4 × 5, 24 = 3 × 8, 30 = 3 × 10.

NameDateTime takenScore ___ / 40
  1. 1.Is 66800 divisible by 20?
  2. 2.Is 36905 divisible by 15?
  3. 3.Is 105889 divisible by 17?
  4. 4.Is 124500 divisible by 18?
  5. 5.Is 3717 divisible by 2?
  6. 6.Is 21390 divisible by 10?
  7. 7.Is 15512 divisible by 4?
  8. 8.Is 12942 divisible by 3?
  9. 9.Is 46937 divisible by 11?
  10. 10.Is 7568 divisible by 8?
  11. 11.Is 9294 divisible by 2?
  12. 12.Is 31932 divisible by 6?
  13. 13.Is 55564 divisible by 29?
  14. 14.Is 1612 divisible by 7?
  15. 15.Is 14104 divisible by 8?
  16. 16.Is 32250 divisible by 6?
  17. 17.Is 36873 divisible by 30?
  18. 18.Is 7101 divisible by 17?
  19. 19.Is 43184 divisible by 7?
  20. 20.Is 106301 divisible by 17?
  21. 21.Is 6872 divisible by 3?
  22. 22.Is 8980 divisible by 2?
  23. 23.Is 40194 divisible by 18?
  24. 24.Is 7359 divisible by 3?
  25. 25.Is 65905 divisible by 13?
  26. 26.Is 60311 divisible by 18?
  27. 27.Is 118556 divisible by 29?
  28. 28.Is 10737 divisible by 3?
  29. 29.Is 91432 divisible by 30?
  30. 30.Is 13817 divisible by 12?
  31. 31.Is 24150 divisible by 10?
  32. 32.Is 198447 divisible by 29?
  33. 33.Is 59280 divisible by 24?
  34. 34.Is 15870 divisible by 30?
  35. 35.Is 66031 divisible by 18?
  36. 36.Is 69257 divisible by 17?
  37. 37.Is 90325 divisible by 13?
  38. 38.Is 2949 divisible by 5?
  39. 39.Is 4394 divisible by 5?
  40. 40.Is 14048 divisible by 8?

Answer key

  1. yes
  2. no
  3. no
  4. no
  5. no
  6. yes
  7. yes
  8. yes
  9. yes
  10. yes
  11. yes
  12. yes
  13. yes
  14. no
  15. yes
  16. yes
  17. no
  18. no
  19. no
  20. yes
  21. no
  22. yes
  23. yes
  24. yes
  25. no
  26. no
  27. no
  28. yes
  29. no
  30. no
  31. yes
  32. yes
  33. yes
  34. yes
  35. no
  36. no
  37. no
  38. no
  39. no
  40. yes

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